Search results for: effective open-loop transfer function (EOTF)

Authors: Truong Nguyen Luan Vu, Moonyong Lee

Abstract:

The interactions between input/output variables are a very common phenomenon encountered in the design of multi-loop controllers for interacting multivariable processes, which can be a serious obstacle for achieving a good overall performance of multiloop control system. To overcome this impediment, the decomposed dynamic interaction analysis is proposed by decomposing the multiloop control system into a set of n independent SISO systems with the corresponding effective open-loop transfer function (EOTF) within the dynamic interactions embedded explicitly. For each EOTF, the reduced model is independently formulated by using the proposed reduction design strategy, and then the paired multi-loop proportional-integral-derivative (PID) controller is derived quite simply and straightforwardly by using internal model control (IMC) theory. This design method can easily be implemented for various industrial processes because of its effectiveness. Several case studies are considered to demonstrate the superior of the proposed method.

Keywords: Multi-loop PID controller, internal model control(IMC), effective open-loop transfer function (EOTF)

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Authors: Myunggon Yoon, Jung-Ho Moon

Abstract:

In this paper, we present a transfer function representation of a general one-dimensional combustor. The input of the transfer function is a heat rate perturbation of a burner and the output is a flow velocity perturbation at the burner. This paper considers a general combustor model composed of multiple cans with different cross sectional areas, along with a non-zero flow rate.

Keywords: Thermoacoustics, dynamics, combustor, transfer function.

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Authors: Tsunwai Gary Yip

Abstract:

Phase locked loops in 10 Gb/s and faster data links are low phase noise devices. Characterization of their phase jitter transfer functions is difficult because the intrinsic noise of the PLLs is comparable to the phase noise of the reference clock signal. The problem is solved by using a linear model to account for the intrinsic noise. This study also introduces a novel technique for measuring the transfer function. It involves the use of the reference clock as a source of wideband excitation, in contrast to the commonly used sinusoidal excitations at discrete frequencies. The data reported here include the intrinsic noise of a PLL for 10 Gb/s links and the jitter transfer function of a PLL for 12.8 Gb/s links. The measured transfer function suggests that the PLL responded like a second order linear system to a low noise reference clock.

Keywords: Intrinsic phase noise, jitter in data link, PLL jitter transfer function, high speed clocking in electronic circuit

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Authors: Tsunwai Gary Yip

Abstract:

Phase locked loops for data links operating at 10 Gb/s or faster are low phase noise devices designed to operate with a low jitter reference clock. Characterization of their jitter transfer function is difficult because the intrinsic noise of the device is comparable to the random noise level in the reference clock signal. A linear model is proposed to account for the intrinsic noise of a PLL. The intrinsic noise data of a PLL for 10 Gb/s links is presented. The jitter transfer function of a PLL in a test chip for 12.8 Gb/s data links was determined in experiments using the 400 MHz reference clock as the source of simultaneous excitations over a wide range of frequency. The result shows that the PLL jitter transfer function can be approximated by a second order linear model.

Keywords: Intrinsic phase noise, jitter in data link, PLL jitter transfer function, high speed clocking in electronic circuit

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Authors: C. Worakitjaroenphon, A. Oonsivilai

Abstract:

The study of piezoelectric material in the past was in T-Domain form; however, no one has studied piezoelectric material in the S-Domain form. This paper will present the piezoelectric material in the transfer function or S-Domain model. S-Domain is a well known mathematical model, used for analyzing the stability of the material and determining the stability limits. By using S-Domain in testing stability of piezoelectric material, it will provide a new tool for the scientific world to study this material in various forms.

Keywords: Piezoelectric, Stability, S-Domain, Transfer function

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Authors: Myung-Gon Yoon, Jung-Ho Moon, Tae Kwon Ha

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This paper studies a robust stabilization problem of a single agent in a multi-agent consensus system composed of identical agents, when the network topology of the system is completely unknown. It is shown that the transfer function of an agent in a consensus system can be described as a multiplicative perturbation of the isolated agent transfer function in frequency domain. From an existing robust stabilization result, we present sufficient conditions for a robust stabilization of an agent against unknown network topology.

Keywords: Multi-agent System, Robust Stabilization, Transfer Function.

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Authors: Te Wen Tu, Sen Yung Lee

Abstract:

An alternative approach is proposed to develop the analytic solution for one dimensional heat conduction with one mixed type boundary condition and general time-dependent heat transfer coefficient. In this study, the physic meaning of the solution procedure is revealed. It is shown that the shifting function takes the physic meaning of the reciprocal of Biot function in the initial time. Numerical results show the accuracy of this study. Comparing with those given in the existing literature, the difference is less than 0.3%.

Keywords: Analytic solution, heat transfer coefficient, shifting function method, time-dependent boundary condition.

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Authors: Jaehyug Lee, Tae-Ho Song

Abstract:

Vacuum Insulation Panel (VIP) can achieve very low thermal conductivity by evacuating its inner space. Heat transfer in the core materials of highly-evacuated VIP occurs by conduction through the solid structure and radiation through the pore. The effect of various scattering modes in combined conduction-radiation in VIP is investigated through numerical analysis. The discrete ordinates interpolation method (DOIM) incorporated with the commercial code FLUENT® is employed. It is found that backward scattering is more effective in reducing the total heat transfer while isotropic scattering is almost identical with pure absorbing/emitting case of the same optical thickness. For a purely scattering medium, the results agrees well with additive solution with diffusion approximation, while a modified term is added in the effect of optical thickness to backward scattering is employed. For other scattering phase functions, it is also confirmed that backwardly scattering phase function gives a lower effective thermal conductivity. Thus the materials with backward scattering properties, with radiation shields are desirable to lower the thermal conductivity of VIPs.

Keywords: Combined conduction and radiation, discrete ordinates interpolation method, scattering phase function, vacuum insulation panel.

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Authors: Chia-Ling Chang, Chung-Sheng Liao

Abstract:

The present study focuses on the discussion over the parameter of Artificial Neural Network (ANN). Sensitivity analysis is applied to assess the effect of the parameters of ANN on the prediction of turbidity of raw water in the water treatment plant. The result shows that transfer function of hidden layer is a critical parameter of ANN. When the transfer function changes, the reliability of prediction of water turbidity is greatly different. Moreover, the estimated water turbidity is less sensitive to training times and learning velocity than the number of neurons in the hidden layer. Therefore, it is important to select an appropriate transfer function and suitable number of neurons in the hidden layer in the process of parameter training and validation.

Keywords: Artificial Neural Network (ANN), sensitivity analysis, turbidity.

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Authors: R. Gunabalan, V. Subbiah

Abstract:

This paper discusses the novel graphical approach for stability analysis of multi induction motor drive controlled by a single inverter. Stability issue arises in parallel connected induction motors under unbalanced load conditions. The two powerful globally accepted modeling and simulation software packages such as MATLAB and LabVIEW are selected to perform the stability analysis. The stability investigation is performed for different load conditions and difference in stator and rotor resistances among the two motors. It is very simple and effective than the techniques presented to obtain the stability of the parallel connected induction motor drive under unbalanced load conditions. Approximate transfer functions are considered to model the induction motors, load dynamics, speed controllers and inverter. Simulink library tools are utilized to model the entire drive scheme in MATLAB. Stability study is discussed in LabVIEW using control design and simulation toolkits. Simulation results are illustrated for various running conditions to demonstrate the effectiveness of the transfer function method.

Keywords: Induction motor, Modeling, Stability analysis, Transfer function model.

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Authors: Clara Shenderey, Helena Vitoshkin, Mordechai Barak, Avraham Arbel

Abstract:

Greenhouse cultivation is an energy-intensive process due to the high demands on cooling or heating according to external climatic conditions, which could be extreme in the summer or winter seasons. The thermal radiation rate inside a greenhouse depends mainly on the type of covering material and greenhouse construction. Using additional thermal screens under a greenhouse covering combined with a dehumidification system improves the insulation and could be cost-effective. Greenhouse covering material usually contains protective ultraviolet (UV) radiation additives to prevent the film wear, insect harm, and crop diseases. This paper investigates the overall heat transfer coefficient, or U-value, for greenhouse polyethylene covering contains UV-additives and glass covering with or without a thermal screen supplement. The hot-box method was employed to evaluate overall heat transfer coefficients experimentally as a function of the type and number of the thermal screens. The results show that the overall heat transfer coefficient decreases with increasing the number of thermal screens as a hyperbolic function. The overall heat transfer coefficient highly depends on the ability of the material to reflect thermal radiation. Using a greenhouse covering, i.e., polyethylene films or glass, in combination with high reflective thermal screens, i.e., containing about 98% of aluminum stripes or aluminum foil, the U-value reduces by 61%-89% in the first case, whereas by 70%-92% in the second case, depending on the number of the thermal screen. Using thermal screens made from low reflective materials may reduce the U-value by 30%-57%. The heat transfer coefficient is an indicator of the thermal insulation properties of the materials, which allows farmers to make decisions on the use of appropriate thermal screens depending on the external and internal climate conditions in a greenhouse.

Keywords: Energy-saving thermal screen, greenhouse covering material, heat transfer coefficient, hot box.

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Authors: Wang Xing-hua, Zhong Shun-an, Zhang Zhuo

Abstract:

A kind of behavior model for discrete sampling and hold amplifier with charge transmission is analyzed. The transfer function and behavior features are based on the main AC responses of operation amplifier. The result used in pipelined and sigma-delta ADC shows the exact of model of sampling and hold amplifier, and the non-ideal factors are taken into account.

Keywords: SHA, response, behavior, transfer function.

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Authors: Leila Graini

Abstract:

In this paper, we demonstrate basic all-optical functions for 2R regeneration (Re-amplification and Re-shaping) based on self-similar spectral broadening in low normal dispersion and highly nonlinear fiber (ND-HNLF) to regenerate the signal through optical filtering including the transfer function characteristics, and output extinction ratio. Our approach of all-optical 2R regeneration is based on those of Mamyshev. The numerical study reveals the self-similar spectral broadening very effective for 2R all-optical regeneration; the proposed design presents high stability compared to a conventional regenerator using SPM broadening with reduction of the intensity fluctuations and improvement of the extinction ratio.

Keywords: All-optical function, 2R optical regeneration, self-similar broadening, Mamyshev regenerator.

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Authors: N. A. Salim, M. M. Othman, I. Musirin, M. S. Serwan

Abstract:

Uncertainty of system operating conditions is one of the causative reasons which may render to the instability of a transmission system. For that reason, accurate assessment of transmission reliability margin (TRM) is essential to ensure effective power transfer between areas during the occurrence of system uncertainties. The power transfer is also called as the available transfer capability (ATC) which is the information required by the utilities and marketers to instigate selling and buying the electric energy. This paper proposes a computationally effective approach to estimate TRM and ATC by considering the uncertainties of system cascading collapse and transmission line outages. In accordance to the results that have been obtained, the proposed method is essential for the transmission providers which could help the power marketers and planning sectors in the operation and reserving transmission services based on the ATC calculated.

Keywords: Available transfer capability, System cascading collapse, Transmission line outages, Transmission reliability margin.

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Authors: Kourosh Parand, Jamal Amani Rad

Abstract:

In this paper, Exp-function method is used for some exact solitary solutions of the generalized Pochhammer-Chree equation. It has been shown that the Exp-function method, with the help of symbolic computation, provides a very effective and powerful mathematical tool for solving nonlinear partial differential equations. As a result, some exact solitary solutions are obtained. It is shown that the Exp-function method is direct, effective, succinct and can be used for many other nonlinear partial differential equations.

Keywords: Exp-function method, generalized Pochhammer- Chree equation, solitary wave solution, ODE's.

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Authors: Sheroz Khan, A. F. Salami, W. A. Lawal, AHM Zahirul Alam, Shihab Abdel Hameed, M. J. E.Salami

Abstract:

In this paper, a multi-branch power line is modeled using ABCD matrix to show its worth as a communication channel. The model is simulated using MATLAB in an effort to investigate the effects of multiple loading, multipath, and those as a result of load mismatching. The channel transfer function is obtained and investigated using different cable lengths, and different number of bridge taps under given loading conditions.

Keywords: Power line Communication, Transfer Function, Channel Modeling, Signal Transmission.

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Authors: S. M. Sohel Murshed, C. A. Nieto de Castro, M. J. V. Lourenço, J. França, A. P. C. Ribeiro, S. I. C.Vieira, C. S. Queirós

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Ionanofluids are a new and innovative class of heat transfer fluids which exhibit fascinating thermophysical properties compared to their base ionic liquids. This paper deals with the findings of thermal conductivity and specific heat capacity of ionanofluids as a function of a temperature and concentration of nanotubes. Simulation results using ionanofluids as coolants in heat exchanger are also used to access their feasibility and performance in heat transfer devices. Results on thermal conductivity and heat capacity of ionanofluids as well as the estimation of heat transfer areas for ionanofluids and ionic liquids in a model shell and tube heat exchanger reveal that ionanofluids possess superior thermal conductivity and heat capacity and require considerably less heat transfer areas as compared to those of their base ionic liquids. This novel class of fluids shows great potential for advanced heat transfer applications.

Keywords: Heat transfer, Ionanofluids, Ionic liquids, Nanotubes, Thermal conductivity.

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Authors: D. H. Lee, Nur Irmawati

Abstract:

This paper aims to study the heat transfer and fluid flow characteristics of nanofluids used in spray cooling systems. The effect of spray height, type of nanofluids and concentration of nanofluids are numerically investigated. Five different nanofluids such as AgH2O, Al2O3, CuO, SiO2 and TiO2 with volume fraction range of 0.5% to 2.5% are used. The results revealed that the heat transfer performance decreases as spray height increases. It is found that TiO2 has the highest transfer coefficient among other nanofluids. In dilute spray conditions, low concentration of nanofluids is observed to be more effective in heat removal in a spray cooling system.

Keywords: Numerical simulation, Spray cooling, Heat transfer, Nanofluids.

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Authors: Wang Liguang, Zhang Xueqing

Abstract:

The build-operate-transfer (BOT) project delivery system has provided effective routes to mobilize private sector funds, innovative technologies, management skills and operational efficiencies for public infrastructure development and have been widely used in China during the last 20 years. Many BOT projects in China will be smoothly transferred to the government soon and the transfer stage, which is considered as the last stage, must be studied carefully and handled well to achieve the overall success of BOT projects. There will be many issues faced by both the public sector and private sector in the transfer stage of BOT projects, including project post-assessment, technology and documents transfer, personal training and staff transition, etc. and sometimes additional legislation is needed for future operation and management of facilities. However, most previous studies focused on the bidding, financing, and building and operation stages instead of transfer stage. This research identifies nine key issues in the transfer stage of BOT projects through a comprehensive study on three cases in China, and the expert interview and expert discussion meetings are held to validate the key issues and give detail analysis. A proposed framework of transfer management is prepared based on the experiences derived and lessons drawn from the case studies and expert interview and discussions, which is expected to improve the transfer management of BOT projects in practice.

Keywords: BOT project, key issues, transfer management transfer stage.

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Authors: N.S. Tomer, Phool Singh, Manoj Kumar

Abstract:

The flow and heat transfer characteristics for natural convection along an inclined plate in a saturated porous medium with an applied magnetic field have been studied. The fluid viscosity has been assumed to be an inverse function of temperature. Assuming temperature vary as a power function of distance. The transformed ordinary differential equations have solved by numerical integration using Runge-Kutta method. The velocity and temperature profile components on the plate are computed and discussed in detail for various values of the variable viscosity parameter, inclination angle, magnetic field parameter, and real constant (λ). The results have also been interpreted with the aid of tables and graphs. The numerical values of Nusselt number have been calculated for the mentioned parameters.

Keywords: Heat Transfer, Magnetic Field, Porosity, Viscosity

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Authors: Tao Nie, Weiqiang Liu

Abstract:

In order to obtain an accurate result of the heat transfer of the rib in the internal cooling Rectangular channel, using separation of variables, analytical solutions of three dimensional steady-state heat conduction in rectangular ribs are given by solving three dimensional steady-state function of the rectangular ribs. Therefore, we can get solution of three dimensional temperature field in the rib. Based on the solution, we can get how the Bi number affected on heat transfer. Furthermore, comparisons of the analytical and numerical results indicate agreement on temperature field in the rib.

Keywords: variable separation method, analytical solution, rib, heat transfer

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Authors: Ahmed Soltan, Ahmed G. Radwan, Ahmed M. Soliman

Abstract:

This work aims to generalize the integer order Sallen-Key filters into the fractional-order domain. The analysis in the case of two different fractional-order elements introduced where the general transfer function becomes four terms which is unusual in the conventional case. In addition, the effect of the transfer function parameters on the filter poles and hence the stability is introduced and closed forms for the filter critical frequencies are driven. Finally, different examples for the fractional order Sallen-Key filter design are presented with circuit simulations using ADS where a great matching between the numerical and simulation results is obtained.

Keywords: Analog Filter, Low-Pass Filter, Fractance, Sallen-Key, Stability.

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Authors: Mihai Brânzei, Ioan Plotog, Ion Pencea

Abstract:

The Pads have unique values of thermophysical properties (THP) having important contribution over heat transfer into the PCB structure. Materials with high thermal diffusivity (TD) rapidly adjust their temperature to that of their surroundings, because the HT is quick in compare to their volumetric heat capacity (VHC). In the paper is presenting the diffusivity tests (ASTM E1461 flash method) for PCBs with different core materials. In the experiments, the multilayer structure of PCBA was taken into consideration, an equivalent property referring to each of experimental structure be practically measured. Concerning to entire structure, the THP emphasize the major contribution of substrate in establishing of reflow soldering process (RSP) heat transfer necessities. This conclusion offer practical solution for heat transfer time constant calculation as function of thickness and substrate material diffusivity with an acceptable error estimation.

Keywords: heat transfer time constant, packaging, reflowsoldering process, thermal diffusivity.

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Authors: Vipul M. Patel, Hemantkumar B. Mehta

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Technological innovations in electronic world demand novel, compact, simple in design, less costly and effective heat transfer devices. Closed Loop Pulsating Heat Pipe (CLPHP) is a passive phase change heat transfer device and has potential to transfer heat quickly and efficiently from source to sink. Thermal performance of a CLPHP is governed by various parameters such as number of U-turns, orientations, input heat, working fluids and filling ratio. The present paper is an attempt to predict the thermal performance of a CLPHP using Artificial Neural Network (ANN). Filling ratio and heat input are considered as input parameters while thermal resistance is set as target parameter. Types of neural networks considered in the present paper are radial basis, generalized regression, linear layer, cascade forward back propagation, feed forward back propagation; feed forward distributed time delay, layer recurrent and Elman back propagation. Linear, logistic sigmoid, tangent sigmoid and Radial Basis Gaussian Function are used as transfer functions. Prediction accuracy is measured based on the experimental data reported by the researchers in open literature as a function of Mean Absolute Relative Deviation (MARD). The prediction of a generalized regression ANN model with spread constant of 4.8 is found in agreement with the experimental data for MARD in the range of ±1.81%.

Keywords: ANN models, CLPHP, filling ratio, generalized regression, spread constant.

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Authors: K. Abbaspoursani, M. Allahyari, M. Rahmani

Abstract:

Thermal conductivity is an important characteristic of a nanofluid in laminar flow heat transfer. This paper presents an improved model for the prediction of the effective thermal conductivity of nanofluids based on dimensionless groups. The model expresses the thermal conductivity of a nanofluid as a function of the thermal conductivity of the solid and liquid, their volume fractions and particle size. The proposed model includes a parameter which accounts for the interfacial shell, brownian motion, and aggregation of particle. The validation of the model is verified by applying the results obtained by the experiments of Tio2-water and Al2o3-water nanofluids.

Keywords: Critical particle size, nanofluid, model, and thermal conductivity.

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Authors: A. Abedian, M. H. Ghiasi, B. Dehghan-Manshadi

Abstract:

A stiffened laminated composite panel (1 m length × 0.5m width) was optimized for minimum weight and deflection under several constraints using genetic algorithm. Here, a significant study on the performance of a penalty function with two kinds of static and dynamic penalty factors was conducted. The results have shown that linear dynamic penalty factors are more effective than the static ones. Also, a specially combined linear-exponential function has shown to perform more effective than the previously mentioned penalty functions. This was then resulted in the less sensitivity of the GA to the amount of penalty factor.

Keywords: Genetic algorithms, penalty function, stiffenedcomposite panel, finite element method.

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Authors: Thandar Aung, Tun Lin Naing

Abstract:

In this paper, the DC-link voltage control of DC-DC boost converter–inverter system is proposed. The mathematical model is developed from four different sub-circuits that depended on the switch positions. The developed differential equations are combined to develop the dynamic model. Transfer function is generated from the switched function model. Fluctuation of DC-link voltage causes connected loads malfunction. For this problem, a kind of traditional controller, the PI controller is applied to achieve constant DC-link voltage. The PI controller gains are obtained based on transfer function step response. The simulation work has been studied by using MATLAB/Simulink software and hardware prototype is implemented with a low-cost microcontroller Arduino Nano. Experimental results are collected by using ArduinoIO library package. Closed-loop DC-link voltage control system is tested with various line and load disturbances. It is found that the experimental results give equal responses with the simulation results.

Keywords: ArduinoIO library package, boost converter-inverter system, low cost microcontroller, PI controller, switched function model.

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Authors: Ahmed, M., Yasser A., Mahmoud H., Ahmed, A., Abdulla M. S., Nazar, S.

Abstract:

Strut-and-Tie Models (STM) for the design of concrete beams, comprising of struts, ties, nodes as the basic tools, is conceptually simple, but its realization for complex concrete structure is not straightforward and depends on flow of internal forces in the structure. STM technique has won wide acceptance for deep member and shear design. STM technique is a unified approach that considers all load effects (bending, axial, shear, and torsion) simultaneously, not just applicable to shear loading only. The present study is to portray Strut-and-Tie Modeling based on Load-Transfer-Mechanisms as a unified method to analyze, design and detailing for deep and slender concrete beams. Three shear span- effective depth ratio (a/ d) are recommended for the modeling of STM elements corresponding to dominant load paths. The study also discusses the research work conduct on effective stress of concrete, tie end anchorage, and transverse reinforcement demand under different load transfer mechanism. It is also highlighted that to make the STM versatile tool for design of beams applicable to all shear spans, the effective stress of concrete and, transverse reinforcement demand, inclined angle of strut, and anchorage requirements of tie bars is required to be correlated with respect to load transfer mechanism. The country code provisions are to be modified and updated to apply for generalized design of concrete deep and slender member using load transfer mechanism based STM technique. Examples available in literature are reanalyzed with refined STM based on load transfer mechanisms and results are compared. It is concluded from the results that proposed approach will require true reinforcement demand depending on dominant force transfer action in concrete beam.

Keywords: Deep member, Load transfer mechanism, Strut-and-Tie Model, Strut, Truss.

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Authors: S.I Sulaiman, T.K Abdul Rahman, I. Musirin, S. Shaari

Abstract:

This paper presents performance analysis of the Evolutionary Programming-Artificial Neural Network (EPANN) based technique to optimize the architecture and training parameters of a one-hidden layer feedforward ANN model for the prediction of energy output from a grid connected photovoltaic system. The ANN utilizes solar radiation and ambient temperature as its inputs while the output is the total watt-hour energy produced from the grid-connected PV system. EP is used to optimize the regression performance of the ANN model by determining the optimum values for the number of nodes in the hidden layer as well as the optimal momentum rate and learning rate for the training. The EPANN model is tested using two types of transfer function for the hidden layer, namely the tangent sigmoid and logarithmic sigmoid. The best transfer function, neural topology and learning parameters were selected based on the highest regression performance obtained during the ANN training and testing process. It is observed that the best transfer function configuration for the prediction model is [logarithmic sigmoid, purely linear].

Keywords: Artificial neural network (ANN), Correlation coefficient (R), Evolutionary programming-ANN (EPANN), Photovoltaic (PV), logarithmic sigmoid and tangent sigmoid.

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Authors: M. Watanabe, T. Yamaguchi, M. Sasajima, Y. Kurosawa, Y. Koike

Abstract:

Earphones and headphones, which are compact electro-acoustic transducers, tend to have a lot of acoustic absorption materials and porous materials known as dampers, which often have a large number of extremely small holes and narrow slits to inhibit the resonance of the vibrating system, because the air viscosity significantly affects the acoustic characteristics in such acoustic paths. In order to perform simulations using the finite element method (FEM), it is necessary to be aware of material characteristics such as the impedance and propagation constants of sound absorbing materials and porous materials. The transfer function is widely known as a measurement method for an acoustic tube with such physical properties, but literature describing the measurements at the upper limits of the audible range is yet to be found. The acoustic tube, which is a measurement instrument, must be made narrow, and the distance between the two sets of microphones must be shortened in order to take measurements of acoustic characteristics at higher frequencies. When such a tube is made narrow, however, the characteristic impedance has been observed to become lower than the impedance of air. This paper considers the cause of this phenomenon to be the effect of the air viscosity and describes an FEM analysis of an acoustic tube considering air viscosity to compare to the theoretical formula by including the effect of air viscosity in the theoretical formula for an acoustic tube.

Keywords: Acoustic tube, air viscosity, earphones, FEM, porous materials, sound absorbing materials, transfer function method.

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